DSC Methods to Quantify Physical Aging and Mobility in Amorphous Systems: Assessing Molecular Mobility

The specific heat capacity (Cp) of amorphous sucrose was determined by DSC after annealing at a particular temperature within the glass transition (Tg) region. The enthalpy recovery after physical aging was obtained from the Cp data through the Tg region after several aging times. This data was fitted to the empirical Williams-Watts equation to obtain values for the mean molecular relaxation time and a parameter for the distribution of relaxation times at the annealing temperature. INTRODUCTION Materials exist in a super-cooled liquid state if they have been melted and then cooled under conditions where they do not crystallize. They are termed amorphous since they are lacking in crystalline order. Their viscosity increases and molecular mobility and specific heat capacity decrease in a complex way as the material is cooled. Their data exhibit an S-shaped curve when measured against temperature and the inflection or midpoint of the S is often termed the glass transition temperature (Tg). The measured value of Tg and the value of these parameters through the Tg region depend on the thermal history of the material. Slow cooling through the Tg region allows adjacent molecules to find configurations of low enthalpy with less excess volume from inefficient packing. Rapid cooling through the Tg region leaves the material in a metastable state with more voids and less favorable intermolecular interactions. This is often illustrated by a diagram showing relative enthalpy (H) of the material as a function of temperature (T) as it is cooled at rapid or slow rates from the melt (Figure 1). Viewed in this way the Tg, as defined by the enthalpy data, decreases as the cooling rate decreases. This relative enthalpy diagram can be generated from DSC data by integrating the Cp or heat flow data. When a material has been cooled rapidly from the melt and is thus in a higher enthalpy state, it will “relax” into a lower enthalpy state when it is held isothermally within the Tg region. This exothermic process is represented in Figure 1 as a vertical arrow at the annealing (or “physical aging”) temperature (Tiso). If the molecular mobility is sufficiently great at the selected temperature, this process can be Figure 1. Tg Enthalpy Diagram of an amorphous material cooled at two rates Tiso H Tg fast cool Tg slow cool ΔH